Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiability

Latent component identification from unknownnonlinearmixtures is a foundational challenge in machine learning, with applications in tasks such as self-supervised learning and causal representation learning. Prior work innonlinear independent component analysis(nICA) has shown that auxiliary signals---such as weak supervision---can supportidentifiabilityof conditionally independent latent components. More recent approaches explore structural assumptions, like sparsity in the Jacobian of the mixing function, to relax such requirements. In this work, we introduceDiverse Influence Component Analysis(DICA), a framework that exploits the convex geometry of the mixing function’s Jacobian. We propose aJacobian Volume Maximization(J-VolMax) criterion, which enables latent component identification by encouraging diversity in their influence on the observed variables. Under suitable conditions, this approach achieves identifiability without relying on auxiliary information, latent component independence, or Jacobian sparsity assumptions. These results extend the scope of identifiability analysis and offer a complementary perspective to existing methods.